It's actually a pretty cool illusion. To really "get it," though, you will need Photoshop, or a similar program with an "eyedropper" tool.
The two squares -- marked A and B -- are seen as different by the eye. A is a "dark" square, and B is a "light" square, based on the pattern of the checkerboard. That distinction is further emphasized by the choice of text color in the square: A has light text on a dark background, and B has dark text on a light background.
However...the two squares really do have the same exact color! The "light" square is made darker by the shadow from the cylinder, and the "dark" square is made lighter by the illumination source. The easiest way to see it is to save the picture, open it in Photoshop, use the eyedropper tool to "pick up" the color from either A or B, and draw in the other square with the paintbrush. You shouldn't be able to see the line, since the two colors are identical!